LDPC Decoding with Offset-Corrected Row LLR Calculation

The patent transforms the complex Sum-Product decoding arithmetic operations into a simplified form by changing the parameter representation from direct logarithmic calculations to minimum-based operations with pre-calculated offsets. The row arithmetic operation is reformulated as: εr,c = min|zr,c′| − offset(r,c), where offset(r,c) = min|zr,c′| − ln(1 + exp(−|zr,c′|)) for the column c′ with the minimum absolute value. This parameter transformation maintains decoding accuracy while dramatically reducing computational complexity.

The patent replaces expensive, complex arithmetic operations with cheaper, simpler operations. Instead of performing full logarithmic calculations and exponential functions, the method uses simple minimum operations and pre-computed offset values. The offset values are calculated once and stored, replacing repeated complex calculations with simple lookups and subtractions, effectively using 'cheap' operations to achieve the same decoding performance.

The patent improves the Offset BP method by refining the offset calculation parameters. Instead of using a fixed or simple offset, the method calculates the offset as offset(r,c) = min|zr,c′| − ln(1 + exp(−|zr,c′|))), where zr,c′ is the column LLR with the minimum absolute value. This parameter refinement captures the non-linear characteristics of the Sum-Product method more accurately, thereby improving decoding precision while maintaining low computational complexity.

The patent incorporates feedback mechanisms by using the minimum absolute value of column LLRs (min|zr,c′|) to dynamically adjust the offset for each row and column combination. This feedback from the actual LLR values allows the offset to adapt to the specific decoding state, improving precision. The offset is recalculated based on the current LLR values, creating a feedback loop that enhances accuracy without requiring full Sum-Product complexity.